Computer simulation of a ceramic core injection molding process

Complex ceramic cores, which form the internal cooling passages of investment-cast turbine blades and used in the aircraft-engine and industrial-gas-turbine industries, are made by ceramic injection molding. The high injection pressure, the high viscosity of the ceramic/wax mixture, and the high injection velocity during the injection molding process result in high rate of erosion, or wear, of the internal surfaces of die. The resurfacing of eroded surfaces of core dies is very costly. In addition to that, inappropriate injection parameters introduce defects, such as weld line and mis-fill, into the quality of the final products. It is desirable to increase the productivity of the ceramic injection molding process and also cut back maintenance costs by evaluating the process performance with computer modeling and simulation to identify means to reduce these problems. In this study, a computer model and simulation of a three-dimensional transient ceramic/wax injection molding (CIM) process including filling and solidification, developed by the Advanced Casting Laboratory at the University of Tennessee for Howmet Research Corporation, was utilized and experimentally validated. The effect of variation of the interfacial heat transfer coefficients on the filling, solidification, and quality of the final products were carefully studied via the computer simulation of the ceramic injection molding process. Experiments were designed and conducted to measure the temperature of ceramic core material as a function of time for both filling and packing stages of the injection molding process. The experiments were conducted under production conditions at Howmet Casting Support in Morristown, Tennessee. The results from the experiments were used to validate the realism and accuracy of the ProCAST simulation of the ceramic core injection molding process. The results from the computer simulations indicated that the interfacial heat transfer coefficient modeled as a ramp function described in this work best represented the experimentally observed thermal characteristics of the filling and solidification process. The flow pattern from this computer simulation yielded a very desirable filling pattern that would avoid the introduction of weld line into the quality of the final product. Also, the computer model predicted the regions of high shear rate and the associated heating where excessive wear of the die was observed. In summary, the model developed was shown to predict successfully the thermal characteristics of the core filling process. The results of this research contributes to the formation of a database of process variables that can be used for control of the injection molding process and for predicting the final geometry as a result of the process

Monte-Carlo simulation of the durability of glass fibre reinforced composite under environmental stress corrosion

The lifetime distribution of glass fibre subject to permanent environmental stress corrosion is very important for assessing the durability and damage tolerance of composites using glass reinforcement. A mechanical model based on the statistics of flaw spectra during stress corrosion and 3D shear lag model is presented. The proposed approach shows that it is possible to identify the influence of stress corrosion properties on the long term durability of glass fibre reinforced composites (GFRP)

A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures

This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement

An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis

This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings

Characterization of graphs whose a small power of their edge ideals has a linear free resolution

Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G)^2$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 3$. Similarly, we show that $I(G)^3$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 4$. We deduce these characterizations from a general formula for the regularity of powers of edge ideals of gap-free graphs $${\rm reg}(I(G)^s) = \max({\rm reg} I(G) + s-1,2s),$$ for $s =2,3$.Comment: 14 pages. Update a proof of Theorem 2.13 with a statement for a squarefree monomial ideal. arXiv admin note: text overlap with arXiv:2109.0639